An optical frequency standard is an optical system that provides an optical signal having a very well defined frequency. These systems have many applications including metrology, astronomy, telecommunications, global positioning systems and scientific research into fundamental physics.
Typically, an optical frequency standard involves stabilising the frequency of a laser to a frequency reference such as an atomic transition having a transition frequency of Two important factors in the performance of an optical frequency standard include its accuracy and its precision or stability. An optical frequency standard's accuracy is typically characterised by how well its output can be related to the unit of the second which is defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. The precision or stability of an optical frequency standard will characterise how reproducible the frequency is between successive measurements or how unchanging it is over various time durations.
In many applications such as metrology and telecommunications, the stability of the optical frequency standard is more important than its inherent accuracy. Where the optical frequency standard involves a laser stabilised to an atomic transition having a transition frequency of f0, the atomic transition will have an associated optical line width of γ. For a given signal to noise ratio (SNR) for detection of the atomic transition, the stability of the optical frequency standard, σ(τ), for a given integration time τ is defined by:
      σ    ⁡          (      τ      )        ∝            γ              f        0              ⁢          1      SNR        ⁢          1              τ            
Accordingly, an optimal stable optical frequency standard will ideally involve a high transition frequency with an associated narrow line width and a large SNR for the system.
One attempt to devise such a stable system has been based on the atomic transition of Rubidium between the energy levels 5S1/2→5D5/2. This transition has a transition frequency f0 of 770.6 THz, i.e. a relatively high frequency, and further has a relatively narrow natural line width γ of 660 kHz. A single photon at f0 of 770.6 THz cannot effectively excite this transition as it does not satisfy the angular momentum selection rules for this transition. However, if two photons, whose own frequencies sum to f0 of 770.6 THz, arrive at the atom nearly simultaneously, then it is possible to drive the transition. Such a process is referred to as a “two-photon” transition. Traditionally, two photons from the laser source are used to drive the transition. Naturally, this means that the frequency of each photon is exactly half that of the energy separation in transition, i.e., 770.6/2 THz=385.3 THz. Referring now to FIG. 1, there is shown the traditional excitation scheme 100 for the 5S1/2→5D5/2 atomic transition for Rubidium showing the two-photon transition from the 5S1/2 state 110 to the 5D5/2 state 120 where the excitation photons each have a wavelength of 778 nm corresponding to 385.3 THz. Detection of the two-photon transition is either by measurement of 778 nm absorption or 420 nm fluorescence as the electron returns to the 5S1/2 state via the intermediate 6P3/2 state 140.
Unfortunately, the 5S1/2→5D5/2 is a weak transition resulting in a relatively low SNR and, as a result, a much reduced stability. As can be seen in FIG. 1, there is an intermediate 5P3/2 state 130 which lies almost midway between the 5S1/2 state 110 and the 5D5/2 state 120. The presence of these intermediate energy levels can greatly increase the transition rate in a two-photon process between the lower and upper energy levels. Unfortunately, if the transition is driven with two photons at the same frequency then there is a large optical detuning of A from the intermediate 5P3/2 state 130 of approximately 1 THz for this excitation scheme. This significant detuning is an important contributor to the weak two-photon transition rate in this instance.
A number of approaches have been adopted in an attempt to increase the SNR of these two-photon systems. These include the use of higher powered lasers and optical cavities to effectively increase laser intensity in the interaction zone and as a result increase the two-photon transition rate and/or increasing the number of Rubidium atoms that the laser can interact with by increasing the Rubidium vapour pressure. Unfortunately, these approaches tend to increase the size, fragility, power consumption or complexity of the resulting system. Many of these approaches also introduce unwanted inaccuracies and imprecision to the system when the performance is considered over the longer term.
This has led to an alternative “two-colour” approach to excitation as contrasted to the “single-colour” approach where the wavelengths of each photon are the same. Referring now to FIG. 2, there is shown an excitation scheme for the 5S1/2→5D5/2 atomic transition similar to FIG. 1, except that the first photon has a wavelength of 780 nm and the second photon has a wavelength of 776 nm. As can be seen from FIG. 2, the detuning relative to the intermediate 5P3/2 state 130 is greatly reduced to as little as approximately 1 GHz, producing an approximate 106 increase in the two-photon transition rate and hence the SNR. In theory, the high optical power and/or optical cavities of single-colour two-photon systems would not be required for a two-colour based system having comparable stability making such an approach potentially suitable for implementation in a compact or portable configuration.
Unfortunately, the standard two-colour approach also has some significant drawbacks in that it is the sum of the two input wavelengths that is stabilised and not either of the individual wavelengths. Put another way, neither the 780 nm nor 776 nm source lasers could be separately employed as a stable optical source—only their sum is stabilised to the two-photon transition.